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A135574
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A024495 but with terms swapped in pairs.
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3
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0, 0, 3, 1, 11, 6, 42, 21, 171, 85, 683, 342, 2730, 1365, 10923, 5461, 43691, 21846, 174762, 87381, 699051, 349525, 2796203, 1398102, 11184810, 5592405, 44739243, 22369621, 178956971, 89478486, 715827882, 357913941, 2863311531, 1431655765
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OFFSET
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0,3
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LINKS
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FORMULA
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O.g.f.: x^2*(3 + x +2*x^2 +3*x^3)/((1-2*x)*(1+2*x)*(x^2-x+1)*(x^2+x+1)). - R. J. Mathar, Mar 31 2008
a(n) = 3*a(n-2) + 3*a(n-4) + 4*a(n-6). - G. C. Greubel, Oct 19 2016
a(n) = (1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*ChebyshevU(n, 1/2) - (1-3*(-1)^n)*ChebyshevU(n-1, 1/2)). - G. C. Greubel, Jan 05 2022
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MAPLE
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A024495 := proc(n) option remember ; if n <=1 then 0; elif n = 2 then 1; else 3*procname(n-1)-3*procname(n-2)+2*procname(n-3) ; fi; end: A135574 := proc(n) option remember ; if n mod 2 = 0 then A024495(n+1) ; else A024495(n-1) ; fi; end: seq(A135574(n), n=0..40) ; # R. J. Mathar, Feb 07 2009
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MATHEMATICA
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LinearRecurrence[{0, 3, 0, 3, 0, 4}, {0, 0, 3, 1, 11, 6}, 41] (* G. C. Greubel, Oct 19 2016 *)
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PROG
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(Magma) I:=[0, 0, 3, 1, 11, 6]; [n le 6 select I[n] else 3*Self(n-2) +3*Self(n-4) +4*Self(n-6): n in [1..41]]; // G. C. Greubel, Jan 05 2022
(Sage) [(1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*chebyshev_U(n, 1/2) - (1-3*(-1)^n)*chebyshev_U(n-1, 1/2)) for n in (0..40)] # G. C. Greubel, Jan 05 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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